Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method

• Дата: 2011
• Автори: Brankov, J.G., Tonchev, N.S.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут фізики конденсованих систем НАН України 2011
• Назва видання: Condensed Matter Physics
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/119801
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Generalized inequalities for the Bogoliubov-Duhamel inner product with applications in the Approximating Hamiltonian Method / J.G. Brankov, N.S. Tonchev // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13003: 1-17. — Бібліогр.: 37 назв. — англ.

Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic fluctuations of intensive observables of a N-particle system and the corresponding Bogoliubov-Duhamel inner product. The novel feature is that, under sufficiently mild conditions, the upper bounds have the same form and order of magnitude with respect to N for all the quantities derived by a finite number of commutations of an original intensive observable with the Hamiltonian. The results are illustrated on two types of exactly solvable model systems: one with bounded separable attraction and the other containing interaction of a boson field with matter.